title: Improving IMRT delivery efficiency with reweighted L1-minimization for inverse planning.
abstract: OBJECTIVE
  This study presents an improved technique to further simplify the fluence-map in intensity modulated radiation therapy (IMRT) inverse planning, thereby reducing plan complexity and improving delivery efficiency, while maintaining the plan quality.
  
  
  METHODS
  First-order total-variation (TV) minimization (min.) based on L1-norm has been proposed to reduce the complexity of fluence-map in IMRT by generating sparse fluence-map variations. However, with stronger dose sparing to the critical structures, the inevitable increase in the fluence-map complexity can lead to inefficient dose delivery. Theoretically, L0-min. is the ideal solution for the sparse signal recovery problem, yet practically intractable due to its nonconvexity of the objective function. As an alternative, the authors use the iteratively reweighted L1-min. technique to incorporate the benefits of the L0-norm into the tractability of L1-min. The weight multiplied to each element is inversely related to the magnitude of the corresponding element, which is iteratively updated by the reweighting process. The proposed penalizing process combined with TV min. further improves sparsity in the fluence-map variations, hence ultimately enhancing the delivery efficiency. To validate the proposed method, this work compares three treatment plans obtained from quadratic min. (generally used in clinic IMRT), conventional TV min., and our proposed reweighted TV min. techniques, implemented by a large-scale L1-solver (template for first-order conic solver), for five patient clinical data. Criteria such as conformation number (CN), modulation index (MI), and estimated treatment time are employed to assess the relationship between the plan quality and delivery efficiency.
  
  
  RESULTS
  The proposed method yields simpler fluence-maps than the quadratic and conventional TV based techniques. To attain a given CN and dose sparing to the critical organs for 5 clinical cases, the proposed method reduces the number of segments by 10-15 and 30-35, relative to TV min. and quadratic min. based plans, while MIs decreases by about 20%-30% and 40%-60% over the plans by two existing techniques, respectively. With such conditions, the total treatment time of the plans obtained from our proposed method can be reduced by 12-30 s and 30-80 s mainly due to greatly shorter multileaf collimator (MLC) traveling time in IMRT step-and-shoot delivery.
  
  
  CONCLUSIONS
  The reweighted L1-minimization technique provides a promising solution to simplify the fluence-map variations in IMRT inverse planning. It improves the delivery efficiency by reducing the entire segments and treatment time, while maintaining the plan quality in terms of target conformity and critical structure sparing.
authors.affiliation: Department of Radiation Oncology, Stanford University, Stanford, California 94305-5847, USA.
authors.forename: Hojin
authors.initials: H
authors.lastname: Kim
authors.forename: Stephen
authors.initials: S
authors.lastname: Becker
authors.forename: Rena
authors.initials: R
authors.lastname: Lee
authors.forename: Soonhyouk
authors.initials: S
authors.lastname: Lee
authors.forename: Sukyoung
authors.initials: S
authors.lastname: Shin
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Candès
authors.forename: Lei
authors.initials: L
authors.lastname: Xing
authors.forename: Ruijiang
authors.initials: R
authors.lastname: Li
mesh_terms: D006801:Humans; D008297:Male; D009369:Neoplasms / Q000532:radiotherapy; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D050397:Radiotherapy, Intensity-Modulated / Q000379:methods*